RepresentationTensor[Subscript[F, 4], Irrep[Subscript[F, 4]][{0, 0, 0, 0}], 
 FundamentalBasis, Irrep[Subscript[F, 4]][{0, 0, 0, 1}] \[CircleTimes] 
  Irrep[Subscript[F, 4]][{0, 0, 0, 1}], FundamentalBasis, 
 {{{0, 0, 0, -2}, Matrix[0, 1, {}]}, {{0, 0, -1, 0}, Matrix[0, 2, {}]}, 
  {{0, 0, -2, 2}, Matrix[0, 1, {}]}, {{0, -1, 1, -1}, Matrix[0, 2, {}]}, 
  {{0, -1, 0, 1}, Matrix[0, 2, {}]}, {{0, -2, 2, 0}, Matrix[0, 1, {}]}, 
  {{-1, 1, -1, -1}, Matrix[0, 2, {}]}, {{-1, 1, -2, 1}, Matrix[0, 2, {}]}, 
  {{-1, 0, 1, -2}, Matrix[0, 2, {}]}, {{-1, 0, 0, 0}, Matrix[0, 6, {}]}, 
  {{-1, 0, -1, 2}, Matrix[0, 2, {}]}, {{-1, -1, 2, -1}, Matrix[0, 2, {}]}, 
  {{-1, -1, 1, 1}, Matrix[0, 2, {}]}, {{-2, 2, -2, 0}, Matrix[0, 1, {}]}, 
  {{-2, 1, 0, -1}, Matrix[0, 2, {}]}, {{-2, 1, -1, 1}, Matrix[0, 2, {}]}, 
  {{-2, 0, 2, -2}, Matrix[0, 1, {}]}, {{-2, 0, 1, 0}, Matrix[0, 2, {}]}, 
  {{-2, 0, 0, 2}, Matrix[0, 1, {}]}, {{1, 0, -1, -1}, Matrix[0, 2, {}]}, 
  {{1, 0, -2, 1}, Matrix[0, 2, {}]}, {{1, -1, 1, -2}, Matrix[0, 2, {}]}, 
  {{1, -1, 0, 0}, Matrix[0, 6, {}]}, {{1, -1, -1, 2}, Matrix[0, 2, {}]}, 
  {{1, -2, 2, -1}, Matrix[0, 2, {}]}, {{1, -2, 1, 1}, Matrix[0, 2, {}]}, 
  {{0, 1, -1, -2}, Matrix[0, 2, {}]}, {{0, 1, -2, 0}, Matrix[0, 6, {}]}, 
  {{0, 1, -3, 2}, Matrix[0, 2, {}]}, {{0, 0, 1, -3}, Matrix[0, 2, {}]}, 
  {{0, 0, 0, -1}, Matrix[0, 12, {}]}, {{0, 0, -1, 1}, Matrix[0, 12, {}]}, 
  {{0, 0, -2, 3}, Matrix[0, 2, {}]}, {{0, -1, 2, -2}, Matrix[0, 6, {}]}, 
  {{0, -1, 1, 0}, Matrix[0, 12, {}]}, {{0, -1, 0, 2}, Matrix[0, 6, {}]}, 
  {{0, -2, 3, -1}, Matrix[0, 2, {}]}, {{0, -2, 2, 1}, Matrix[0, 2, {}]}, 
  {{-1, 2, -2, -1}, Matrix[0, 2, {}]}, {{-1, 2, -3, 1}, Matrix[0, 2, {}]}, 
  {{-1, 1, 0, -2}, Matrix[0, 6, {}]}, {{-1, 1, -1, 0}, Matrix[0, 12, {}]}, 
  {{-1, 1, -2, 2}, Matrix[0, 6, {}]}, {{-1, 0, 2, -3}, Matrix[0, 2, {}]}, 
  {{-1, 0, 1, -1}, Matrix[0, 12, {}]}, {{-1, 0, 0, 1}, Matrix[0, 12, {}]}, 
  {{-1, 0, -1, 3}, Matrix[0, 2, {}]}, {{-1, -1, 3, -2}, Matrix[0, 2, {}]}, 
  {{-1, -1, 2, 0}, Matrix[0, 6, {}]}, {{-1, -1, 1, 2}, Matrix[0, 2, {}]}, 
  {{-2, 2, -1, -1}, Matrix[0, 2, {}]}, {{-2, 2, -2, 1}, Matrix[0, 2, {}]}, 
  {{-2, 1, 1, -2}, Matrix[0, 2, {}]}, {{-2, 1, 0, 0}, Matrix[0, 6, {}]}, 
  {{-2, 1, -1, 2}, Matrix[0, 2, {}]}, {{-2, 0, 2, -1}, Matrix[0, 2, {}]}, 
  {{-2, 0, 1, 1}, Matrix[0, 2, {}]}, {{2, 0, -2, 0}, Matrix[0, 1, {}]}, 
  {{2, -1, 0, -1}, Matrix[0, 2, {}]}, {{2, -1, -1, 1}, Matrix[0, 2, {}]}, 
  {{2, -2, 2, -2}, Matrix[0, 1, {}]}, {{2, -2, 1, 0}, Matrix[0, 2, {}]}, 
  {{2, -2, 0, 2}, Matrix[0, 1, {}]}, {{1, 1, -2, -1}, Matrix[0, 2, {}]}, 
  {{1, 1, -3, 1}, Matrix[0, 2, {}]}, {{1, 0, 0, -2}, Matrix[0, 6, {}]}, 
  {{1, 0, -1, 0}, Matrix[0, 12, {}]}, {{1, 0, -2, 2}, Matrix[0, 6, {}]}, 
  {{1, -1, 2, -3}, Matrix[0, 2, {}]}, {{1, -1, 1, -1}, Matrix[0, 12, {}]}, 
  {{1, -1, 0, 1}, Matrix[0, 12, {}]}, {{1, -1, -1, 3}, Matrix[0, 2, {}]}, 
  {{1, -2, 3, -2}, Matrix[0, 2, {}]}, {{1, -2, 2, 0}, Matrix[0, 6, {}]}, 
  {{1, -2, 1, 2}, Matrix[0, 2, {}]}, {{0, 2, -2, -2}, Matrix[0, 1, {}]}, 
  {{0, 2, -3, 0}, Matrix[0, 2, {}]}, {{0, 2, -4, 2}, Matrix[0, 1, {}]}, 
  {{0, 1, 0, -3}, Matrix[0, 2, {}]}, {{0, 1, -1, -1}, Matrix[0, 12, {}]}, 
  {{0, 1, -2, 1}, Matrix[0, 12, {}]}, {{0, 1, -3, 3}, Matrix[0, 2, {}]}, 
  {{0, 0, 2, -4}, Matrix[0, 1, {}]}, {{0, 0, 1, -2}, Matrix[0, 12, {}]}, 
  {{0, 0, 0, 0}, Matrix[1, 28, 
    {{q^22/((1 + q^8)*(1 + q^2 + q^4 + q^12 + q^14 + q^16 + q^18 + q^20 + 
         q^22 + q^24 + q^32 + q^34 + q^36)), 
      -(q^21/((1 + q^8)*(1 + q^2 + q^4 + q^12 + q^14 + q^16 + q^18 + q^20 + 
          q^22 + q^24 + q^32 + q^34 + q^36))), 
      q^20/((1 + q^8)*(1 + q^2 + q^4 + q^12 + q^14 + q^16 + q^18 + q^20 + 
         q^22 + q^24 + q^32 + q^34 + q^36)), 
      -(q^18/((1 + q^8)*(1 + q^2 + q^4 + q^12 + q^14 + q^16 + q^18 + q^20 + 
          q^22 + q^24 + q^32 + q^34 + q^36))), 
      q^17/((1 + q^8)*(1 + q^2 + q^4 + q^12 + q^14 + q^16 + q^18 + q^20 + 
         q^22 + q^24 + q^32 + q^34 + q^36)), 
      -((q^15*(1 + q^2))/((1 + q^8)*(1 + q^2 + q^4 + q^12 + q^14 + q^16 + 
          q^18 + q^20 + q^22 + q^24 + q^32 + q^34 + q^36))), 
      q^16/((1 + q^8)*(1 + q^2 + q^4 + q^12 + q^14 + q^16 + q^18 + q^20 + 
         q^22 + q^24 + q^32 + q^34 + q^36)), 
      -(q^15/((1 + q^8)*(1 + q^2 + q^4 + q^12 + q^14 + q^16 + q^18 + q^20 + 
          q^22 + q^24 + q^32 + q^34 + q^36))), (q^13*(1 + q^2))/
       ((1 + q^8)*(1 + q^2 + q^4 + q^12 + q^14 + q^16 + q^18 + q^20 + q^22 + 
         q^24 + q^32 + q^34 + q^36)), 
      q^13/((1 + q^8)*(1 + q^2 + q^4 + q^12 + q^14 + q^16 + q^18 + q^20 + 
         q^22 + q^24 + q^32 + q^34 + q^36)), 
      -((q^11*(1 + q^2))/((1 + q^8)*(1 + q^2 + q^4 + q^12 + q^14 + q^16 + 
          q^18 + q^20 + q^22 + q^24 + q^32 + q^34 + q^36))), 
      -(q^12/((1 + q^8)*(1 + q^2 + q^4 + q^12 + q^14 + q^16 + q^18 + q^20 + 
          q^22 + q^24 + q^32 + q^34 + q^36))), (q^9*(1 + q^2))/
       ((1 + q^8)*(1 + q^2 + q^4 + q^12 + q^14 + q^16 + q^18 + q^20 + q^22 + 
         q^24 + q^32 + q^34 + q^36)), 
      q^10/((1 + q^8)*(1 + q^2 + q^4 + q^12 + q^14 + q^16 + q^18 + q^20 + 
         q^22 + q^24 + q^32 + q^34 + q^36)), 
      q^10/((1 + q^8)*(1 + q^2 + q^4 + q^12 + q^14 + q^16 + q^18 + q^20 + 
         q^22 + q^24 + q^32 + q^34 + q^36)), (q^9*(1 + q^2))/
       ((1 + q^8)*(1 + q^2 + q^4 + q^12 + q^14 + q^16 + q^18 + q^20 + q^22 + 
         q^24 + q^32 + q^34 + q^36)), 
      -(q^10/((1 + q^8)*(1 + q^2 + q^4 + q^12 + q^14 + q^16 + q^18 + q^20 + 
          q^22 + q^24 + q^32 + q^34 + q^36))), 
      -((q^9*(1 + q^2))/((1 + q^8)*(1 + q^2 + q^4 + q^12 + q^14 + q^16 + 
          q^18 + q^20 + q^22 + q^24 + q^32 + q^34 + q^36))), 
      q^9/((1 + q^8)*(1 + q^2 + q^4 + q^12 + q^14 + q^16 + q^18 + q^20 + 
         q^22 + q^24 + q^32 + q^34 + q^36)), (q^7 + q^9)/
       ((1 + q^8)*(1 + q^2 + q^4 + q^12 + q^14 + q^16 + q^18 + q^20 + q^22 + 
         q^24 + q^32 + q^34 + q^36)), 
      -(q^7/((1 + q^8)*(1 + q^2 + q^4 + q^12 + q^14 + q^16 + q^18 + q^20 + 
          q^22 + q^24 + q^32 + q^34 + q^36))), 
      q^6/((1 + q^8)*(1 + q^2 + q^4 + q^12 + q^14 + q^16 + q^18 + q^20 + 
         q^22 + q^24 + q^32 + q^34 + q^36)), 
      -((q^5*(1 + q^2))/((1 + q^8)*(1 + q^2 + q^4 + q^12 + q^14 + q^16 + 
          q^18 + q^20 + q^22 + q^24 + q^32 + q^34 + q^36))), 
      q^5/((1 + q^8)*(1 + q^2 + q^4 + q^12 + q^14 + q^16 + q^18 + q^20 + 
         q^22 + q^24 + q^32 + q^34 + q^36)), 
      -(q^4/((1 + q^8)*(1 + q^2 + q^4 + q^12 + q^14 + q^16 + q^18 + q^20 + 
          q^22 + q^24 + q^32 + q^34 + q^36))), 
      q^2/((1 + q^8)*(1 + q^2 + q^4 + q^12 + q^14 + q^16 + q^18 + q^20 + 
         q^22 + q^24 + q^32 + q^34 + q^36)), 
      -(q/((1 + q^8)*(1 + q^2 + q^4 + q^12 + q^14 + q^16 + q^18 + q^20 + 
          q^22 + q^24 + q^32 + q^34 + q^36))), 
      1/((1 + q^8)*(1 + q^2 + q^4 + q^12 + q^14 + q^16 + q^18 + q^20 + q^22 + 
         q^24 + q^32 + q^34 + q^36))}}]}, {{0, 0, -1, 2}, Matrix[0, 12, {}]}, 
  {{0, 0, -2, 4}, Matrix[0, 1, {}]}, {{0, -1, 3, -3}, Matrix[0, 2, {}]}, 
  {{0, -1, 2, -1}, Matrix[0, 12, {}]}, {{0, -1, 1, 1}, Matrix[0, 12, {}]}, 
  {{0, -1, 0, 3}, Matrix[0, 2, {}]}, {{0, -2, 4, -2}, Matrix[0, 1, {}]}, 
  {{0, -2, 3, 0}, Matrix[0, 2, {}]}, {{0, -2, 2, 2}, Matrix[0, 1, {}]}, 
  {{-1, 2, -1, -2}, Matrix[0, 2, {}]}, {{-1, 2, -2, 0}, Matrix[0, 6, {}]}, 
  {{-1, 2, -3, 2}, Matrix[0, 2, {}]}, {{-1, 1, 1, -3}, Matrix[0, 2, {}]}, 
  {{-1, 1, 0, -1}, Matrix[0, 12, {}]}, {{-1, 1, -1, 1}, Matrix[0, 12, {}]}, 
  {{-1, 1, -2, 3}, Matrix[0, 2, {}]}, {{-1, 0, 2, -2}, Matrix[0, 6, {}]}, 
  {{-1, 0, 1, 0}, Matrix[0, 12, {}]}, {{-1, 0, 0, 2}, Matrix[0, 6, {}]}, 
  {{-1, -1, 3, -1}, Matrix[0, 2, {}]}, {{-1, -1, 2, 1}, Matrix[0, 2, {}]}, 
  {{-2, 2, 0, -2}, Matrix[0, 1, {}]}, {{-2, 2, -1, 0}, Matrix[0, 2, {}]}, 
  {{-2, 2, -2, 2}, Matrix[0, 1, {}]}, {{-2, 1, 1, -1}, Matrix[0, 2, {}]}, 
  {{-2, 1, 0, 1}, Matrix[0, 2, {}]}, {{-2, 0, 2, 0}, Matrix[0, 1, {}]}, 
  {{2, 0, -1, -1}, Matrix[0, 2, {}]}, {{2, 0, -2, 1}, Matrix[0, 2, {}]}, 
  {{2, -1, 1, -2}, Matrix[0, 2, {}]}, {{2, -1, 0, 0}, Matrix[0, 6, {}]}, 
  {{2, -1, -1, 2}, Matrix[0, 2, {}]}, {{2, -2, 2, -1}, Matrix[0, 2, {}]}, 
  {{2, -2, 1, 1}, Matrix[0, 2, {}]}, {{1, 1, -1, -2}, Matrix[0, 2, {}]}, 
  {{1, 1, -2, 0}, Matrix[0, 6, {}]}, {{1, 1, -3, 2}, Matrix[0, 2, {}]}, 
  {{1, 0, 1, -3}, Matrix[0, 2, {}]}, {{1, 0, 0, -1}, Matrix[0, 12, {}]}, 
  {{1, 0, -1, 1}, Matrix[0, 12, {}]}, {{1, 0, -2, 3}, Matrix[0, 2, {}]}, 
  {{1, -1, 2, -2}, Matrix[0, 6, {}]}, {{1, -1, 1, 0}, Matrix[0, 12, {}]}, 
  {{1, -1, 0, 2}, Matrix[0, 6, {}]}, {{1, -2, 3, -1}, Matrix[0, 2, {}]}, 
  {{1, -2, 2, 1}, Matrix[0, 2, {}]}, {{0, 2, -2, -1}, Matrix[0, 2, {}]}, 
  {{0, 2, -3, 1}, Matrix[0, 2, {}]}, {{0, 1, 0, -2}, Matrix[0, 6, {}]}, 
  {{0, 1, -1, 0}, Matrix[0, 12, {}]}, {{0, 1, -2, 2}, Matrix[0, 6, {}]}, 
  {{0, 0, 2, -3}, Matrix[0, 2, {}]}, {{0, 0, 1, -1}, Matrix[0, 12, {}]}, 
  {{0, 0, 0, 1}, Matrix[0, 12, {}]}, {{0, 0, -1, 3}, Matrix[0, 2, {}]}, 
  {{0, -1, 3, -2}, Matrix[0, 2, {}]}, {{0, -1, 2, 0}, Matrix[0, 6, {}]}, 
  {{0, -1, 1, 2}, Matrix[0, 2, {}]}, {{-1, 2, -1, -1}, Matrix[0, 2, {}]}, 
  {{-1, 2, -2, 1}, Matrix[0, 2, {}]}, {{-1, 1, 1, -2}, Matrix[0, 2, {}]}, 
  {{-1, 1, 0, 0}, Matrix[0, 6, {}]}, {{-1, 1, -1, 2}, Matrix[0, 2, {}]}, 
  {{-1, 0, 2, -1}, Matrix[0, 2, {}]}, {{-1, 0, 1, 1}, Matrix[0, 2, {}]}, 
  {{2, 0, 0, -2}, Matrix[0, 1, {}]}, {{2, 0, -1, 0}, Matrix[0, 2, {}]}, 
  {{2, 0, -2, 2}, Matrix[0, 1, {}]}, {{2, -1, 1, -1}, Matrix[0, 2, {}]}, 
  {{2, -1, 0, 1}, Matrix[0, 2, {}]}, {{2, -2, 2, 0}, Matrix[0, 1, {}]}, 
  {{1, 1, -1, -1}, Matrix[0, 2, {}]}, {{1, 1, -2, 1}, Matrix[0, 2, {}]}, 
  {{1, 0, 1, -2}, Matrix[0, 2, {}]}, {{1, 0, 0, 0}, Matrix[0, 6, {}]}, 
  {{1, 0, -1, 2}, Matrix[0, 2, {}]}, {{1, -1, 2, -1}, Matrix[0, 2, {}]}, 
  {{1, -1, 1, 1}, Matrix[0, 2, {}]}, {{0, 2, -2, 0}, Matrix[0, 1, {}]}, 
  {{0, 1, 0, -1}, Matrix[0, 2, {}]}, {{0, 1, -1, 1}, Matrix[0, 2, {}]}, 
  {{0, 0, 2, -2}, Matrix[0, 1, {}]}, {{0, 0, 1, 0}, Matrix[0, 2, {}]}, 
  {{0, 0, 0, 2}, Matrix[0, 1, {}]}}]
